1. Field of the Invention
The present invention relates to a demodulator for digital transmission, in which symbols are transmitted by phase modulation, or by amplitude and phase modulation.
2. Discussion of the Related Art
In an ideal carrier-modulation wide-band digital transmission, each transmitted symbol is formed by one or several periods of a sinusoid, where one parameter among the amplitude, frequency and/or phase has been modified, the modified parameter being only able to take a limited number of discrete values.
In the case of an ideal wide-band phase modulation, the transmitted modulated signal v complies with the following relation:v(t)=A cos(2πft+φ(t))  (1)
where f is the carrier frequency, A is the signal amplitude, and φ is the signal phase. The spectrum of the modulated signal corresponds to the baseband signal spectrum shifted around the carrier frequency with a suppression of the latter. Equation (1) can be written as:v(t)=A[cos 2πft*cos φ(t)−sin πft*sin φ(t)]  (2)
Equation (2) corresponds to the sum of two amplitude-modulated carriers in quadrature. Generally, equation (1) can be written as:v(t)=Re(aej(2πft+φ))=Re(aejφej2πft)  (3)
Complex amplitude aejφ is represented, in the complex plane, by a point having its coordinates I and Q given by the following relation:I=a×cos φ and Q=a×sin φ  (4)
For an ideal M-state phase-modulation digital transmission, phase φ can take discrete values from among M values, which corresponds to M points or states in the complex plane. The arrangement of points in the complex plane is called a constellation. The number of bits that can be coded for each transmitted symbol is equal to Log2(M).
FIG. 1 shows an example of a constellation for an ideal four-state phase modulation or QPSK (Quadrature Phase Shift Keying) modulation. Each transmitted symbol corresponds to one of the four phase states and carries a two-bit word information. As an example, in FIG. 1, the sequence of bits coded by each state has been shown next to said state.
The transmitted modulated signal can be written as:v(t)=x cos 2πft+y sin 2πft  (5)
where x and y are equal to ±1. Such a modulation is frequently used in digital telephony.
FIG. 2 shows an example of a conventional demodulator 10 for phase-modulation digital transmission. Demodulator 10 receives a modulated signal v at an input terminal IN. Signal v is provided to a unit 12 (tuner) for transferring the signal in baseband. The operation of the baseband transfer unit requires determination of the frequency of the carrier used for the modulation of the transmitted symbols. Unit 12 provides two analog signals I*, Q* which correspond, in the complex plane of the constellation, to components of a complex signal s. Signals I*, Q* are converted into digital signals I*n, Q*n by analog-to-digital converters 14 (AD) controlled by a sampling clock signal CLK. Given the inaccuracies and the fluctuations on determination of the carrier used by unit 12, an additional correction must generally be performed on digital signals I*n, Q*n to correct a frequency shift of the carrier, which will be called hereafter a carrier shift. A carrier shift translates as a rotation of the constellation in the complex plane. A correction of the carrier shift is performed by a carrier shift correction loop 16 which comprises a correction unit 18 (corrector) which corrects signals I*n, Q*n and drives an adapted filter 20 which provides filtered digital signals In, Qn. A carrier offset estimation unit 22 receives digital signals In, Qn and determines an error signal representative of the carrier shift. The carrier shift error signal is transmitted to a filter 24 (carrier loop filter) which provides a control signal to correction unit 18.
Another correction should be performed due to the fact that, in practice, the implemented phase modulation is not an ideal phase modulation. Such a correction concerns the determination of the sampling times of signals I*n, Q*n provided by unit 12. Indeed, to limit the passband of the modulated signal, the carrier modulation is not performed by an abrupt switching from one state to another of the constellation but by a continuous transition between the constellation states. It is thus desirable for signals I*, Q* to be sampled at optimal times corresponding to the passing of signal s through states of the constellation and not at times corresponding to transitions between two states. Such a correction is performed by a timing correction loop 26. Timing correction loop 26 comprises a timing error estimation device 28 which receives signals In, Qn and provides an error signal Errn to a filter 30 (timing loop filter). Filter 30 provides a control signal Com to a voltage-controlled oscillator 32 (VCO) which provides sampling clock signal CLK to analog-to-digital converters 14 at a sampling frequency which depends on control signal Com.
There are several examples of timing error estimation devices. A first device example implements the Gardner algorithm (defined in the publication entitled “A BPSK/QPSK Timing Error Detector for Sampled Receivers”, IEEE Transactions of Communications, Vol. Com-34, pages 423-429, May 1986). Such an error estimation device provides an error signal according to the following relation:Errn=In[In+1/2−In−1/2]+Qn[Qn+1/2−Qn−1/2]  (6)
where n represents the index of the considered symbol. Such a determination of the error signal has the advantage of being independent from the phase of the carrier and thus accepts a significant carrier frequency shift. The provision of a usable error signal Errn thus does not require for the carrier shift correction loop 16 to have converged. However, a disadvantage of such a timing error estimation is that it requires determination, for a symbol of index n, of two additional inter-symbol values noted by indexes n±½.
Another example of a timing error estimation device uses the Mueller and Müller algorithm (defined in the publication entitled “Timing Recovery in Digital Synchronous Data Receivers”, IEEE Transactions on Communications, Vol. Com-26, pages 516-531, May 1976). The Mueller and Müller algorithm requires for an assumption to be made on the value of the complex signal corresponding to components In, Qn, for example, considering that the constellation point closest to the sampled symbol corresponds to that which should be received. Such an error estimation has the advantage of not requiring determination of additional inter-symbol values between two sampled symbols. However, it has two significant disadvantages: the first one is that the constellation must be known, the second one is that it is sensitive to a shift of the carrier and thus requires for the carrier shift correction loop to have converged.